In various disciplines such as ultrasound reflectometry, medical imaging using sonography, radar, seismology, echocardiography and other similar areas, a common problem exists in that waveform data obtained in these areas will often include reflections from adjacent obstacles which will often overlap the desired echo or reflected signals. The overlapping echo waveforms tend to obscure the desired signals and result in lower resolution which inhibits effective and accurate interpretation of the data. I ultrasound reflectometry which is used for medical imaging as well as non-destructive testing applications, such obscuring echoes result in the inability to form high resolution images thereby degrading the diagnostic capabilities achievable by the procedure. Medical imaging has become an important aspect of present day medical technology and presently includes techniques such as X-ray tomography, magnetic resonance imaging (MRI) or CAT-scan techniques which themselves require relatively high cost, elaborate equipment and processing capabilities which inhibit their effective use in many situations. If higher resolution and improved ultrasound images could be obtained, this technique may considerably reduce the cost as compared to other imaging techniques while providing more accurate diagnostics in medicine.
Ultrasound has been known to be applicable for medical imaging as well as non-destructive testing as it is a mechanical wave phenomena wherein a medium under test will enable generated ultrasonic pulses or waves to propagate therein. In medical imaging techniques such a medium will be the soft tissue of the body with reflecting objects being the internal organs thereof. The waveforms used in ultrasound reflectometry as well as medical sonography are typically several cycles in length and are rapidly damped to a few wavelengths, at the resonant frequency of the transducer. The transducer is typically a piezoelectric crystal which gives rise to a sonic wave propagating into the medium under study and reflecting as echoes from reflecting surfaces within the medium which are detected by the reverse of the piezoelectric effect. In medical sonography for example, the transducer normally serves as both a transmitter and a receiver, and therefore induced vibrations must be damped quickly to avoid a very long ring-down time in order to receive echo signals. When low frequencies are chosen to obtain low attenuation of the waveforms through the medium under test, then the time waveforms of reflections from adjacent obstacles will often overlap. The overlap of echoes makes it difficult to interpret where the sources of the echoes are located and results in extremely difficult signal processing problems to obtain high resolution data which avoids the contribution of unwanted overlapping echo information.
One processing technique being echo envelope processing has been utilized, but it has been found that the received information is still significantly contaminated by obscuring overlapping echoes. The overlapping echo waveform phenomena resulting from the low frequencies chosen for ultrasound reflectometry as based upon attenuation and resolution constraints have been noted in literature such as found in an article by R. C. Kemerait and D. G. Childers entitled "Signal Detection and Extraction By Cepstrum Techniques" IEEE Transactions on Information Theory, Volume II-18, No. 6, pp. 745-749, November, 1972, as well as a publication by J. Blitz, entitled "Ultrasonics: Methods and Applications", Van Nostrand Reinhold Company, New York, 1971. In the first of these publications, there is set forth a technique for decomposing a composite signal of unknown multiple wavelets which overlap in time. Several prior procedures for achieving the decomposition of superimposed signals include inverse filtering wherein a signal is transformed by a linear time-invariant system, whose Fourier transform is the reciprocal of the transform of the signal components to be removed. In such a method, the signal must be known and the signal to noise ratio must be quite large. Decision Theory has also been used to decompose superimposed signals to estimate the echo amplitude and arrival times, but only if the signal wave shape is known. If the wavelet waveshape and number of echoes are unknown, other techniques have been looked to. The Cepstrum techniques of echo detection accomplish decomposition by means of a function of the power spectrum of the received signals to determine the timing and relative amplitudes of echoes in the system. The signal waveform is then extracted by means of complex Cepstrum techniques.
It has also been found that phase information can be used in the estimation of time delays between two received signals as described in an article by A. G. Piersol, entitled "Time Delay Estimation Using Phase Data", IEEE Transactions on Acoustics, Speech and Signal Processing, Volume ASSP-29, No. 3, pp. 471-477, June 1981. Such an estimation of time delays between two received signals using phase measurements relied upon the use of straightforward regression analysis procedures on phase estimates at properly selected frequencies in the frequency domain. Such analysis of the phase information was found to yield time delay estimates having realistic error assessments based upon non-parametric variance calculations.
Similarly, a publication by T. F. Quatieri, Jr. and A. B. Oppenheim, entitled "Iterative Techniques for a Minimum Phase Signal Reconstruction from Phase or Magnitude", IEEE Transactions on Acoustics, Speech and Signal Processing, Volume ASSP-29, No. 6, pp. 1187-1193, December, 1981, develops iterative algorithms for reconstructing a signal from a partial specification thereof in the time or frequency domains. The technique utilizes iterative algorithms for reconstructing a minimum or maximum phase signal from the phase or magnitude of its Fourier transform. Additionally, a phase unwrapping algorithm is proposed which is implemented by applying the Hilbert transform to the logarithmic value of the Fourier transform of a minimum phase sequence.
Although the information content of the phase component of systems has been recognized in different applications, the phase unwrapping techniques have inhibited their effective use with respect to processing in ultrasound reflectometry or similar systems where obscuring overlapping echoes degrade resolution. For example, in a publication by E. Poggiagliomi, A. J. Berkhout, M. M. Boone, entitled "Phase Unwrapping, Possibilities and Limitations", Geophysical Prospecting, No. 30, pp. 281-291, 1982, a phase unwrapping technique is set forth wherein the phase spectrum can only be correctly unwrapped between notches in the amplitude spectrum and other experimental difficulties are also present in the described method.
Some researchers have turned to the principle of Maximum Entropy, which involves autoregressive modeling, and which has been applied successfully to generate power spectral estimations. In publication by J. P. Burg, entitled "Maximum Entropy Spectral Analysis", Modern Spectrum Analysis, edited by D. G. Childers, IEEE Press, New York, pp. 34-41, 1978. Comparison of the maximum entropy method to some traditional techniques was analyzed in a book by A. V. Oppenheim and R. W. Schafer, entitled "Digital Signal Processing, Printice-Hall, Englewood Cliffs, New Jersey, 1975, wherein the maximum entropy method was found to produce higher frequency resolution and yield data of better dependability as it depends only upon the available data and requires simplified storage requirements owing to the infinite impulse response structure of the resulting all pole filter. The all pole filter is found to yield a smoothly changing phase estimate, which does not appear to have the experimental difficulties reported with various other methods to obtain phase estimates. Such a method has been studied by N. Erdol in a PhD dissertation entitled "Use of the Maximum Entropy Method for Phase Estimation" at the University of Akron, Akron, Ohio. In this study, it was found that phase information obtained by using maximum entropy spectral estimates could be utilized to subsequently obtain delay information from the maximum entropy phase estimation by means of discrete Fourier transformation techniques.